bv_cvxbook_extra_exercises

Give the optimal cost obtained c sa and compare to

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Unformatted text preview: d make use of all available edges.” 134 16 Energy and power 16.1 Power flow optimization with ‘N − 1’ reliability constraint. We model a network of power lines as a graph with n nodes and m edges. The power flow along line j is denoted pj , which can be positive, which means power flows along the line in the direction of the edge, or negative, which means power flows along the line in the direction opposite the edge. (In other words, edge orientation is only used to determine the direction in which power flow is considered positive.) Each edge can support power flow in either direction, up to a given maximum capacity Pjmax , i.e., we have |pj | ≤ Pjmax . Generators are attached to the first k nodes. Generator i provides power gi to the network. These must satisfy 0 ≤ gi ≤ Gmax , where Gmax is a given maximum power available from generator i. i i The power generation costs are ci > 0, which are given; the total cost of power generation is cT g . Electrical loads are connected to the nodes k + 1, . ....
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